Ole Gunnar Solskjaer made his first signing of the summer on Wednesday, with Donny van de Beek joining the Red Devils in a £40million switch from Ajax.
After securing a third-place Premier League finish in his first full season at Old Trafford, Solskjaer will be determined to compete with title favourites Liverpool and Manchester City this term.
And Meulensteen, who worked as part of Sir Alex Ferguson’s coaching staff from 2007-2013, believes signing Kane will allow the Norwegian to mount a title challenge.
“What is vitally important is that United have a really good start to the season, so that they don’t lose any ground, they are in there and they keep competing, because that will grow the belief,” he told talkSPORT.
“I keep saying they should bring in a really top, top striker.
“For example, if they would be able to get Kane - I don’t think they will get him - but if they would get Kane, I would say they will compete for the title next year.”
Kane, 27, has scored 188 goals in 287 appearances for Tottenham, while also scoring 32 goals in 45 games for England.
The Three Lions captain has been linked with a move to United in the past, yet Spurs are highly unlikely to sell their star man with four years remaining on his current contract.
And should they continue with their pursuit of £100million-rated Sancho, the Red Devils would find it difficult to afford him in the current climate.
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United are also said to be in the mix to sign highly-rated Sevilla defender Diego Carlos this summer, although they face competition from bitter rivals Liverpool.
According to Spanish outlet Marca, both clubs are interested in signing the 27-year-old - who has a £68million release clause in his Sevilla contract.